Senior executives from some the world’s largest technology firms were meeting face to face with Barack Obama on Tuesday to press their case for a major rollback of National Security Agency surveillance.

The White House is hosting the 15-strong delegation from Silicon Valley, which includes the chief executives of Apple, Yahoo and Google, less than 24 hours after a federal judge ruled that the NSA program to collect telephone metadata is likely to be unconstitutional.

Many of the senior tech leaders meeting the president and the vice-president, Joe Biden, have already made public their demand for sweeping surveillance reforms in an open letter that specifically called for a ban on the kind of bulk data collection that the judge ruled on Monday was probably unlawful.

Judge Richard Leon’s ruling, which will now be subject to an appeal, is the most significant legal setback for the agency since the publication of the first surveillance disclosures by the whistleblower Edward Snowden, and it comes at a pivotal moment for the future of the NSA.

The president and his advisers are currently considering the recommendations of an NSA review panel set up in the wake of Snowden’s revelations.

Obama, a former constitutional lawyer who opposed excessive government surveillance as a US senator, must now grapple with the findings of a damning court ruling that concludes that mass collection of phone records probably violates the fourth amendment – which prohibits unreasonable searches and seizures – and is “almost Orwellian” in its scope. Leon said James Madison, who played a key role in drafting the US constitution, would be “aghast” at the scope of the agency’s collection of Americans' communications data.

The decision by the tech giants to press their case in such a public and unified way is a significant moment in the debate over NSA surveillance. The industry is an increasingly influential voice in Washington. The tech sector is a vital part of the US economy and many of its most successful leaders are prominent Democratic political donors, including to the campaign that secured Obama’s re-election.

The White House said that in addition to discussing “national security and the economic impacts of unauthorised intelligence disclosures”, the meeting with executives cover technical aspects of the administration’s rollout of healthcare reforms and wider issues relating to the economy. However, the meeting is likely to be dominated by discussions about the NSA, particularly the phone metadata program and its collection of data.

Among those meeting at the White House are Tim Cook, the CEO of Apple, Marissa Mayer, the CEO of Yahoo, and Eric Schmidt, Google’s executive chairman. Senior representatives from Comcast, Facebook, Microsoft, Twitter, and Netflix will also be in attendance. So too will Randall Stephenson, the chairman and CEO of AT&T, one of the telecom providers routinely required to provide the NSA with so-called metadata about its US customers.

With legislation to reform the NSA currently stalled on Capitol Hill, and unlikely to resurface until January, privacy advocates are focused on the White House, which could enact its own changes if the president is persuaded of the need. An intense lobbying effort has gone on for months, with senior figures in the intelligence community warning that any significant dilution of its powers will risk another terrorist attack on the scale of 9/11.

The review panel, which handed its findings to Obama on Friday, has reportedly proposed only limited reforms, saying the NSA’s surveillance tools should be amended in light of Snowden’s disclosures but essentially remain intact. One decisive factor in the president's considerations could be the White House’s recent appointment of John Podesta, Bill Clinton’s former chief of staff.

Podesta, whose role as éminence grise to the president begins next month, has gone on the record saying Obama should establish a “national commission” to respond to the legitimate concerns raised by Snowden’s disclosures. Podesta added in an interview with Der Spiegel in July: “Surely we can meet our national security needs without sacrificing the respect for personal privacy that has long been a hallmark of American life?”

Specifically, Podesta expressed concern about the relevance of legal precedents being used to justify massive data collection on the digital era, a view apparently in sync with Monday’s damning court ruling. “In the United States, court decisions from the pre-internet days suggest that the information we give away voluntarily to these companies can be obtained fairly easily by the government,” he said.

“That legal rule may have made sense in an age before Facebook and iPhones, but we need a serious examination of whether it still makes sense today.”

Hours before Tuesday's meeting, Snowden released an open letter to Brazil, offering to shed light on US spying in return for political asylum. Snowden currently has temporary asylum. The White House has rejected the suggestion that administration might offer him amnesty.

The idea of an amnesty in return for Snowden securing data was floated by Richard Ledgett, the senior NSA official tasked managing the fallout from Snowden’s leaks – and a potential candidate to become the new director of the spy agency.